A Resistive Linear Antenna for Ground-Penetrating Radars
Kangwook Kim and Waymond R. Scott, Jr.
School of Electrical and Computer Engineering
Georgia Institute of Technology
Atlanta, Georgia 30332-0250
ABSTRACT
The resistive vee dipole (RVD) loaded with the Wu-King profile has many advantages for use in groundpenetrating radar (GPR) applications. It can be designed to transmit a temporally-short pulse to a small
spot on the ground. The shape of the transmitted pulse is simply related to the input signal, e.g., a derivative.
The RVD also has a low radar cross section. In addition, it can be easily manufactured using a circuit board and
discretely loading it with chip resistors. One drawback of the RVD is that the input impedance of the RVD increases significantly with decreasing frequency and, therefore, has a high voltage standing wave ratio (VSWR) at
low frequencies, which limits the low-frequency response of the antenna. To improve the low-frequency response,
a discretely-loaded resistive linear antenna (RLA) has been developed, whose basic principle of operation is the
same as that of the RVD. The RLA has curved arms loaded with a modified Wu-King profile instead of straight
arms loaded with the Wu-King profile. With an appropriate selection of the curve and the loading profile, the
low-frequency response is significantly better for the RLA than for the RVD. The RLA has been developed using
a method of moments code. The performance of the RLA is validated both numerically and experimentally.
Keywords: Loaded antenna, resistive vee dipole (RVD), ground-penetrating radar (GPR)
1. INTRODUCTION
A resistively-loaded vee dipole (RVD) is a vee dipole with each arm loaded with a resistive profile.1–3 In a
short-pulse ground-penetrating radar (GPR) application, the Wu-King profile is usually chosen for the resistive
profile because an RVD with the Wu-King profile can be made to radiate a short pulse into a small spot on
the ground while having a low radar cross section.4–8 In addition, it is geometrically simple and light; thus, it
can be easily applied to an array application for a hand-held system with a small number of elements or for a
vehicle-mounted system with a large number of elements.9
However, the RVD has several drawbacks. First, the input impedance of the RVD increases significantly with
decreasing frequency and, therefore, has a high voltage standing wave ratio (VSWR) at low frequencies. This
limits the low frequency response of the antenna. Another drawback is that it is difficult to build an RVD with
a continuous resistive profile while being mechanical strong. We have previously developed a way to build a
mechanically-strong RVD with an accurate resistive profile and demonstrated its performance.9 In the previous
work, the antenna arms were printed on a thin Kapton film and surface-mount chip resistors were loaded such
that they approximate the continuous resistive profile. The antenna was then attached to a thick FR-4 frame
to enhance the mechanical strength. While this antenna had an accurate resistive profile, the structure needed
improvement because delicate components such as chip resistors were exposed.
In this paper, we present a resistive linear antenna (RLA), which is an improved version of the RVD. To
improve the VSWR, we used curved arms instead of straight arms and loaded the arms with a modified WuKing resistive profile. This also improves other characteristics, such as the gain and front-to-back ratio. The
mechanical reliability is improved by inserting the antenna between two blocks of polystyrene foam instead of
attaching it to an FR-4 frame. The resulting structure is more robust and easier to handle because all the
delicate components are covered by the polystyrene foam.
Further author information: (Send correspondence to K. Kim)
K. Kim: E-mail: kangwook.kim@ece.gatech.edu, Telephone: 1 404 894 3123
W. R. Scott: E-mail: waymond.scott@ece.gatech.edu, Telephone: 1 404 894 3048
Detection and Remediation Technologies for Mines and Minelike Targets IX, edited by
Russell S. Harmon, J. Thomas Broach, John H. Holloway, Jr., Proceedings of SPIE Vol. 5415
(SPIE, Bellingham, WA, 2004) 0277-786X/04/$15 · doi: 10.1117/12.542694
359
2
R0 / R'
Modified
Wu-King
(continuous)
Modified
Wu-King
(discretized)
1
Wu-King
(continuous)
0
0
1
r' / h
Figure 1. Resistive loading profiles of the continuous Wu-King, continuous modified Wu-King, and discrete modified
Wu-King in terms of conductivity.
2. ANTENNA DESIGN
The Wu-King resistive profile (R ) can be written as the resistance per unit length as:
R (r ) =
R0
,
1 − (r /h)
(1)
where r is the distance along the arm from the drive point, h is the length of the arm, and R0 is the resistance
per unit length at the drive point. With an appropriate selection of R0 , a current pulse injected into the RVD
travels with a negligible internal reflection. However, a current pulse incident in the feed line is significantly
reflected by the Wu-King profile at the drive point because the resistance per unit length jumps from zero in
the feed line to R = R0 at the drive point (r = 0). This reflection can be lowered by selecting a lower R0 than
the appropriate value. However, this will lower the resistive profile throughout the entire arm, which increases
reflection at the open end of the antenna.
In order to lower R at the drive point while maintaining small open-end reflection, the Wu-King profile is
modified to
2 −1
/h)
/h)]
1
−
(r
[1
−
(r
(r ) =
+
,
(2)
Rm
R0
R0m
where R0m is a parameter that modifies the resistive profile. This equation is equivalent to Eq. (1) when
at the drive point decreases with decreasing R0m , while Rm
at the antenna open end
R0m = ∞. In Eq. (2), Rm
always converges to R (r = h). In this work, we choose R0m /R0 = 1.0. The modified Wu-King profile with
R0m /R0 = 1.0 is compared with the original Wu-King profile in Fig. 1. The figure shows that the resistance per
unit length of the modified Wu-King profile at the drive point is reduced to half of that of the original Wu-King
(0) = 0.5R (0)). Both profiles converge to infinity at the antenna open end.
profile (Rm
Another reason for currents to be reflected at the drive point is that the geometry changes abruptly from a
feed line to the antenna. Thus, the reflection can be reduced by smoothly changing the antenna shape from the
feed line. In this work, the shape of the RLA varies according to the following equations:
0 ≤ z < z0 ,
y1 = aebz ,
(3)
y=
2
z0 ≤ z ≤ L.
y2 = c0 + c1 (z − z0 ) + c2 (z − z0 ) ,
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Proc. of SPIE Vol. 5415
L = 17.15cm
y
bz
y2 = c0 + c1(z-z0)
2
+ c2(z-z0)
z
feed line
(coplanar stripline)
w=
3mm
z0 = 0.2L
2Ap = 16.33cm
y1 = ae
2A = 11.43cm
2a = 1.585mm
y2 = c0 + c1(z-z0)
Figure 2. Description of the antenna shape. The solid lines show the designed antenna shape. The dotted lines on the
right-hand side show the shape of the antenna if the curve were straight over the interval z0 ≤ z ≤ L.
Fig. 2 shows the diagram of the antenna generated from these equations. The curve grows exponentially over
the interval 0 < z ≤ z0 and grows at a slower rate over the interval z0 ≤ z ≤ L, where L is the length of the
antenna in the z-direction. The antenna is fed by a coplanar stripline with the characteristic impedance Z0 .
The parameter a is determined such that the drive point of the antenna has the same characteristic impedance
as the feed line, when the antenna resistive loading is ignored. The parameters b, c0 , c1 , and c2 are determined
according to the following relations:
aebz0 = c0 ,
bz0
abe
= c1 ,
y1 = y2 at z = z0 ,
y1 = y2 at z = z0 ,
c0 + c1 (L − z0 ) = Ap ,
ȳ2 = Ap at z = L,
c0 + c1 (L − z0 ) + c2 (L − z0 )2 = A,
y2 = A at z = L,
(4)
where Ap is a half of the aperture size if the curve were straight over the interval z0 ≤ z ≤ L, and A is a
half of the aperture size. In this work, the chosen parameters are Z0 = 200Ω, 2A = 11.43cm, 2Ap = 16.33cm,
L = 17.15cm, and z0 /L = 0.2. The width of the stripline is chosen to be 3mm. Thus, the coplanar stripline
geometry at the drive point requires 2a = 1.585mm to have Z0 = 200Ω.10 The parameters determined from
Eqs. (3) and (4) are b = 67.34, c0 = 0.007976, c1 = 0.5371, and c2 = −1.302.
3. NUMERICAL ANALYSIS
Three antennas are numerically analyzed using EIGER, a method of moments code.11 The antennas are an RVD
with straight arms and continuous Wu-King profile, the RLA with curved arms and continuous modified WuKing profile, and the RLA with curved arms and discrete modified Wu-King profile. The common parameters for
the antennas are length L = 17.15cm, aperture size 2A = 11.43cm, width of striplines w = 3mm, and resistance
per unit length normalized by the arm length R0 h = 467.1Ω. For the RLA with discrete profile, the continuous
profile is discretized by 14 resistors, whose values are marked by rectangles in Fig. 1. The resistors are modeled
by a patch with an appropriate surface resistance; the width and length of each patch are 1.25mm and 1.2mm,
respectively. In this section, the antennas are fed by a 200Ω transmission line.
Fig. 3 shows the VSWR’s of the antennas. The VSWR of the RLA is significantly lowered at low frequencies,
essentially extending the lower end of the bandwidth. The bandwidth with VSWR = 2.0 begins at 1.19GHz
Proc. of SPIE Vol. 5415
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3.0
VSWR
2.5
RLA (continuously loaded)
RLA (discretely loaded)
RVD (continuously loaded)
2.0
1.5
1.0
0
2
4
6
Frequency, GHz
8
10
Figure 3. Voltage standing wave ratios of the continuously loaded RVD, continuously loaded RLA, and discretely loaded
RLA as functions of frequency.
for the RLA with discretized loading and 1.64GHz for the RVD with continuous loading. The bandwidth with
VSWR = 1.5 begins at 2.23GHz for the RLA with discretized loading and 3.76GHz for the RVD with continuous
loading. Note that the VSWR for the RLA with discretized profile is slightly worse than the other antennas for
frequencies higher than 8GHz. The reason for this is the resonant frequency of the resistor spacing. The length
of the antenna arm along the curve is 19.1cm. With 14 resistors, the average resistor spacing is 1.36cm. The
first resonant frequency of this spacing is approximately 11GHz. The effect of the resonant behavior begins to
appear at 10GHz in the figure. This behavior gives a rough guideline on how many resistors need to be used.
Clearly, the more number of resistors need to be used if one wants a broader bandwidth.
Fig. 4 shows the gains of the antennas as functions of frequency. Here, the gain is defined as
gain = 4π
radiation intensity
.
power incident in the feed line
(5)
The figure shows that the RLA’s have higher gains than the RVD. The discretization of the loading profile does
not seem to affect the gain much for frequencies less than 8GHz. The gain of the RLA is deteriorated by the
discretization at frequencies higher than 8GHz. Note that the gains are relatively low for all the three antennas.
The reason for this is that a large portion of the incident energy is dissipated in the resistors as well as reflected
at the drive point.5, 12 Thus, the radiation efficiencies of the antennas are low.
The low radiation efficiency of the antenna is not a problem for a GPR because of the close proximity to
the targets. The reflections from the equipment behind the antenna and the multiple reflections between the
antenna and the surface of the ground are bigger issues. The rejection of the signals from behind an antenna,
such as the reflected signal from the equipment, can be measured by the front-to-back ratio (F/B). Fig. 5 shows
the F/B’s of the antennas in a dB-scale. The F/B of the RLA is higher for most frequencies than that of the
RVD. The improvement is significant around 2GHz for both continuously and discretely loaded RLA’s. The
improvement at 2GHz may be particularly useful because the GPR in this work depends much on the frequency
content around this frequency.
The multiple reflections between the antenna and the surface of the ground can be lowered by designing the
antenna to be less reflective, e.g., to have low RCS at the boresight angle. Fig. 6 shows the monostatic RCS
observed at the boresight of the antenna. The RCS is improved at most frequencies with use of the curved
arms and continuous modified Wu-King profile. However, the RCS is deteriorated by the discretization of the
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Proc. of SPIE Vol. 5415
10
Gain, dB
0
-10
RLA (continuously loaded)
RLA (discretely loaded)
RVD (continuously loaded)
-20
0
2
4
6
Frequency, GHz
8
10
Figure 4. Gains of the continuously loaded RVD, continuously loaded RLA, and discretely loaded RLA in dB.
40
F / B, dB
30
20
RLA (continuously loaded)
RLA (discretely loaded)
RVD (continuously loaded)
10
0
0
2
4
6
Frequency, GHz
8
10
Figure 5. Front-to-back ratios of the continuously loaded RVD, continuously loaded RLA, and discretely loaded RLA in
dB.
Proc. of SPIE Vol. 5415
363
-10
RLA (continuously loaded)
RLA (discretely loaded)
RVD (continuously loaded)
s / (2A)2, dB
-20
-30
-40
-50
0
2
4
6
Frequency, GHz
8
10
Figure 6. Radar cross sections of the continuously loaded RVD, continuously loaded RLA, and discretely loaded RLA
in dB. The RCS’s are normalized by the aperture length squared.
continuous profile. Note that the RCS for the discretely loaded RLA is still comparable to the RCS for the RVD
over the frequency range 1.5GHz < f < 7GHz.
Finally, Fig. 7 shows the gain patterns of the antennas in the E- and H-planes at eight frequency points.
Each curve is normalized by its maximum and drawn on a 30dB-scale. Fig. 7 (c) shows that the backward
radiation of the RLA is negligible at f = 2GHz, which is also shown in Fig. 5. In Figs. 7 (d) – (h), back lobes
are seen for the RLA’s; however, their normalized amplitudes are smaller than backward radiation of the RVD.
Note that in Figs. 7 (d) – (h), nulls are seen around 90◦ both in the E- and H-planes. This may result in less
coupling between adjacent elements in an array.
4. ANTENNA MEASUREMENT
The RLA with discretized loading profile has been manufactured. The antenna arms are printed on a 50.8µmthick (2mil) Kapton substrate. Each arm is loaded with 14 surface-mount chip resistors, whose width and length
are 1.25mm and 2.0mm, respectively∗ . The resistors approximate the continuous profile over the operating
frequency band. The antenna is fed by a double-Y balun/transformer, whose characteristic impedance at the
antenna drive point is approximately 188Ω.13 Note that the antenna structure made in this method is very
fragile. In the previous work, we attached the antenna structure to a thick FR-4 frame to enhance the mechanical
strength.9 The resulting structure was strong enough to be used in the experiment with care. However, it may
not be usable in the field because the resistors are exposed and prone to damage. Thus, in this work, we
increased the mechanical reliability of the antenna by squeezing it between two 2.54cm-thick polystyrene foam
blocks. Fig. 8 shows the implemented antenna structure. Because all the delicate parts are shielded by the
polystyrene foam blocks, this structure may be used in the field.
The performance of the manufactured antenna is measured in terms of VSWR and gain. The measurement is
compared with the numerical results. Fig. 9 shows the VSWR of the RLA when the RLA is connected to a 188Ω
feed line, which is the output characteristic impedance of the double-Y balun used in this work. The graph shows
that the manufactured RLA works very well. Fig. 10 shows the gain of the antenna module (RLA and balun).
For the gain measurement, two identically-manufactured antennas are used. The antennas are separated by a
distance R and pointed at each other. Then, the transmission coefficient (S21 ) is measured at each frequency.
∗
The resistors are terminated with 0.4mm-long metal leads at both ends. Thus, the effective length of the resistive
film is 1.2mm, which is the dimension used for the length of the resistive patch in the numerical model.
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Proc. of SPIE Vol. 5415
E-plane
0°
E-plane
H-plane
90°
90°
E-plane
0°
90°
90°
0.5GHz
1.0GHz
180°
(a)
180°
(b)
0°
90°
E-plane
H-plane
90°
H-plane
0°
90°
H-plane
90°
2.0GHz
3.0GHz
180°
(c)
180°
(d)
RLA (continuously loaded)
RLA (discretely loaded)
RVD (continuously loaded)
Figure 7. Normalized gain patterns of the continuously loaded RVD, continuously loaded RLA, and discretely loaded
RLA in a 30-dB scale. The left- and right-hand sides of each graph are the gain patterns observed in the principal Eand H-planes, respectively.
Proc. of SPIE Vol. 5415
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E-plane
0°
E-plane
H-plane
90°
90°
E-plane
90°
5.0GHz
180°
(e)
180°
(f)
0°
E-plane
H-plane
90°
0°
90°
7.0GHz
180°
(g)
180°
(h)
RLA (discretely loaded)
RVD (continuously loaded)
Figure 7. Continued.
H-plane
90°
6.0GHz
RLA (continuously loaded)
Proc. of SPIE Vol. 5415
H-plane
90°
4.0GHz
90°
366
0°
Kapton
film
2.54cm-thick
Styrofoam
balun /
transformer
chip
resistors
(a)
(b)
Figure 8. Photographs of the RLA: (a) antenna and balun on a polystyrene foam block; and (b) antenna and balun
squeezed between two blocks of polystyrene foam.
3.0
VSWR
2.5
Measurement
Theory (MoM)
2.0
1.5
1.0
0
2
4
6
Frequency, GHz
8
10
Figure 9. Comparison of the measured VSWR and numerical VSWR of the manufactured antenna when it is connected
to a 188Ω feed line.
Because the gain is identical for both antennas, it can be obtained by inverting the following equation at each
frequency:
2
λ
,
(6)
|S21 |2 = G0 (f )2
4πR
where G0 (f ) is the gain of the antenna at a frequency, and λ is the wavelength at the frequency.14 The figure
shows that the antenna module performs well at low frequencies. Its performance is degraded at high frequencies
because of the loss in the balun.
The use of the RLA in a GPR is demonstrated by forming a bistatic radar using the two antennas separated
by 11.43cm and pointing them toward the same direction. Four landmines, i.e., VS-1.6, VS-50, TS-50, and
VS-2.2, are used as buried targets, which are buried along the y-direction at depths 6cm, 1cm, 1cm, and 6cm
from the surface, respectively. The GPR is scanned approximately 2cm high above the ground (Fig. 11). The
response is obtained as functions of y-coordinate and frequency. The y and frequency grids consist of 91 points
Proc. of SPIE Vol. 5415
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10
Gain, dB
0
-10
Measurement
Theory (MoM)
-20
0
2
4
6
Frequency, GHz
8
10
Figure 10. Comparison of the measured and numerical gains of the manufactured antenna. In the numerical model, the
antenna is fed by a 200Ω balanced transmission line, and the gain is measured at the drive point. In the measurement,
the antenna is fed by the double-Y balun, and the gain is measured at the balun input port.
Figure 11. Photograph of the two identical RLA’s forming a GPR. The two antennas are separated by 11.43cm and
fixed to a plastic rod, which is connected to a position controller.
with 2cm increment and 401 points from 500MHz to 8.5GH with 20MHz increment, respectively. The frequency
response is then transformed to the time domain for a differentiated Gaussian pulse incident in the feed line with
the center frequency of 2.5GHz.
The experiment was performed at the Electromagnetics/Acoustics Laboratory at the Georgia Institute of
Technology. Fig. 12 shows the results in a pseudo-color image, which plots the received voltage in the space-time
domain. The horizontal axis represents the y-coordinate, and the vertical axis represents the time. The big
horizontal response centered at 1.6nsec is the return from the surface of the ground. The landmines are clearly
seen later in time. The first reflections from the 1cm-deep targets are seen around 1.8nsec, and the first reflections
from the 6cm-deep targets are seen around 2.75nsec. The speed of wave propagation in the test soil is roughly
a third of the speed of light in free space. For large targets such as VS-1.5 and VS-2.2, the reflections from the
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Proc. of SPIE Vol. 5415
VS-1.6
VS-50
TS-50 VS-2.2
-50
1
t, nsec
-60
3
Intensity, dB
2
-70
4
5
-90
-45
0
y, cm
45
90
-80
Figure 12. GPR scan result of the landmines in a pseudo-color graph. The graph shows the signal intensities in a 30-dB
scale. The vertical axis represent the time, and the horizontal axis represent the position of the GPR. The lines above
the pseudo-color graph show the relative sizes and depths of the landmines schematically.
top and bottom of the target are distinguishable.
5. CONCLUSION
The RVD was improved and referred to as RLA in this work. The RLA was shown to perform better than
the RVD in terms of VSWR, gain, and F/B. The RLA was comparable to the RVD in terms of RCS. The
improvement was achieved by using curved arms loaded with a modified Wu-King profile instead of straight
arms loaded with the Wu-King profile.
The designed antenna was manufactured by printing the arms on a thin Kapton film and loading them with
chip resistors. The antenna arms and the balun were squeezed between two polystyrene foam blocks to enhance
the mechanical strength and to protect the delicate components. The performance of the manufactured antenna
was validated by measurements. The use of the RLA in a bistatic GPR was also demonstrated.
ACKNOWLEDGMENTS
This work is supported in part by the US Army Night Vision and Electronic Sensors Directorate, Science and
Technology Division, Countermine Branch and in part by the U. S. Army Research Office under Contract Number
DAAD19-02-1-0252.
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